III 77
Logical Necessity/Armstrong: ist the strongest form - physical necessity: is weaker, because it is contingent! - Even weaker: universal quantification (is a mere regularity.) - Important Argument: it is impossible to infer from a law to universal quantification. - Law: physical necessity.
III 96
Necessity/Universals/Armstrong: now we can clarify the concept of necessity between universals. - We translate "N(F,G)" (the assertion of a state, which is at the same time a relationship) as follows: the F-ness of something makes the G-ness of the same thing necessary by virtue of the universals F and G.
That is not simply: universal quantification: for all x, x". F-ness makes it necessary that x is G - that would regularity theory. >
Regularity Theory.
Necessity/Armstrong: exists rather between types than between tokens: the F-ness of something, not a"s F-ness.
III 163
Necessity/Possible Worlds/Armstrong: possible worlds do not need "possibilia" themselves. - Necessity: does not have to be equal in all possible worlds!
In some possible worlds the necessity might not apply. A law of nature can have different status in different possible worlds.
Notation: "square" N": necessity in all possible worlds - (strong necessity)
III 166
Weak necessity: not all possible worlds - Notation:"necessary (square) ("Socrates exists > Socrates is human)" (operator before the entire conditional. (>
Range/Scope).
III 164
ArmstrongVsStrong N: requires U to be necessary - but Universals are contingent - III 165 VsStrong Necessity in possible worlds where there are no Fs and Gs it is obliged to uninstantiated universals.
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Place II 59
Necessity/Place: (conceptualist): only de dicto! - Only type of de re: causal necessity: but contrast here is not contingency, but independence - whether causal need is present, is observed a posteriori (therefore contingent) - contingent: i.e. the dependence was causal or it was not.
Place II 59
Necessity/de dicto: (a priori): can something be denied without contradiction? (Linguistic question) - according to this criterion: token identity: typically contingent - type identity: typically necessary - Conceptualism/Place: contingent hypotheses of type-identity become a necessary truth, when the conventional criteria of attribution of universals change.
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II (c) 95
Necessity/Armstrong: stems only from identity! - Logical possibility: is not possible between separate entities (E.g. cause/effect) - (This is controversial).
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Martin II 135
Necessity/Contingency/Quine/Martin: puts both on the same level (like many precursors). Quine, early: seemed to tip towards the side of contingency, Quine, late: according to the necessity: Figures for physics, or principle of identity of empirically isomorphic theories.